More complex models of selection Spatial variation Temporal variation Frequency-dependence

1. More complex models of selection Spatial variation Temporal variation Frequency-dependence

2. spatially heterogeneous selection patch type A1A1 A1A2 A2A2 i 1 + s 1 1 – s j 1 – s 1 1 + s initially, f(A1) = 1 in all patches introduce A2 at low frequency pr(polymorphism) -- relative frequency of patch types -- strength and symmetry of selection -- initial allele frequencies (some models) -- dispersal capabilities of the organism

3. temporal heterogeneity in selection -- random fluctuations -- long-term change -- regular oscillations A1A1 A1A2 A2A2 wet 1 1 1-s dry 1-t 1 1

4. frequency-dependent selection frequency-dependent predation random predation fitness advantage when rare disadvantage when common frequency eaten [output] frequency in array [input] common rare

5. frequency-dependent selection A1A1 A1A2 A2A2 geno. freq. p2 2pq q2 wij 1-tp2 1-2tpq 1-tq2 wij 1-p2 1-2pq 1-q2 wij is a function of frequency: (1-t)(fij) = wij lim w22 1 and lim w22 0 q 0q 1

6. (1-t)(fij) = wij relative fitness, wij frequency, f(AiAj) at equilibrium allele frequencies, all genotypes can have the same fitness w is not necessarily maximized at equilibrium

7. frequency dependent selection in the cichlid Peridossus microlepis (Hori 1993)

8. P. microlepis eats scales from living fish mouth is asymmetrical: left- or right- mouthed ‘mouthedness’ determined by a single locus with 2 alleles – dextral (DD, Dd) is dominant to sinistral (dd) prey right-mouthed (dextral) left-mouthed (sinistral) Lake Tanganyika 2 sites, 7 km apart follow populations for 11 years, sampling at 1-2 year intervals

9. fluctuations in the frequency of left-mouthed fish

10. explanation: prey fish learn which side to protect, depending on which morph of P. microlepis is common null hypothesis: no learning response by prey, success by the two morphs of P. microlepis is either equal or proportional to their frequency alternate hypothesis: the common morph will have lower success than the rare morph test by measuring success rates at times when each morph is common

11. dextral attacks sinistral attacks

12. frequency-dependent selection may be widespread self-incompatibility alleles in plants apostatic selection by predators mimicry complexes (negative f-d when the mimic is palatable; positive f-d when the mimic is distasteful sexual reproduction and parasites sexual selection sex determination in haplodiploids

13. spatial heterogeneity can maintain a genetic polymorphism - relative frequency of patch types - relative strength of selection within patch types - dispersal capabilities of the organism temporal heterogeneity will maintain genetic variation under certain conditions - random fluctuations or (slow) long-term change in selection pressures promote genetic polymorphisms - regular oscillations (i.e., seasonality) in selection tend to eliminate all but one allele from the population frequency-dependent selection - negative frequency-dependent selection will maintain a polymorphism with dynamic (vs. stable) allele frequencies - frequency-dependent selection may be widespread in nature